Question

AD is an altitude of an equilateral triangle ABC. On AD as base, another equilateral triangle ADE is constructed. Prove that Area (ΔADE): Area (ΔABC) = 3: 4

Answer 1

We have,
ΔABC is an equilateral triangle
Then, AB = BC = AC
Let, AB = BC = AC = 2x
Since, AD ⊥ BC then BD = DC = x
In ΔADB, by Pythagoras theorem

By area of similar triangle theorem